James Kemp

This plugin allows you to list any number of related posts from the same category as the current post. You can also randomise these results. It is very lightweight, at only 3KB.
There are a number of options available:
<ul>
<li>Choose the number of Posts to show</li>
<li>Choose whether it displays these posts randomly, or in order specified by you.</li>
<li>Choose whether to display a title, what tags to use, and what text should be displayed (e.g. H3)</li>
<li>Choose a class for the main UL</li>
</ul>
To display the random related posts in its simplest form, simply place the following code in your single.php file – <code><?php relatedPosts(); ?></code>.
To edit the options availble, use the following codes:
<pre><code><?php relatedPosts(
 $ppp = 4, 
 $rand = true, 
 $rPinctitle = true, 
 $rPtitletag = 'h3', 
 $rPtitle = 'Related Posts', 
 $rPulclass = 'related_posts',
 $orderby = 'title', 
 $order = 'ASC'
); ?>
</code></pre>
Where:
<ul>
<li>$ppp = Number of posts to display (Any integer allowed)</li>
<li>$rand = sets the display to random (true/false)</li>
<li>$rPinctitle = Displays the title (true/false)</li>
<li>$rPtitletag = The type of tag to wrap the title in (Default h3, but it can be any valid HTML tag)</li>
<li>$rPtitle = The title to be displayed (This can be any text value)</li>
<li>$rPulclass = This sets the class of the ul (This can be any text value)</li>
<li>$rPexcerpt = Displays the post excerpt (true/false)</li>
<li>$orderby = This allows you to order the posts by certain parameters (title/author/date/modified/menu_order/parent/ID/none/comment_count) If you want to choose the order of your posts, be sure to set $rand to false</li>
<li>$order = This can either be Ascending or Descending (ASC/DESC)</li>
</ul>

Random Related Posts Based on Category

This plugin allows you to list any number of related posts from the same category as the current post. You can also randomise these results.

keesiemeijer

Quickly increase your readers’ engagement by adding related posts in the sidebar or after post content with a widget or shortcode.
Posts with the most terms in common will display at the top!
This plugin is capable of finding related posts in multiple taxonomies and post types. Include or exclude terms from the search for related posts. Change the look and feel by using your own templates in a (child) theme.
<a href="http://keesiemeijer.wordpress.com/related-posts-by-taxonomy/" rel="nofollow ugc">plugin documentation</a>
Plugin features:
<ul>
<li>Widget and Shortcode.</li>
<li>Display related posts as post thumbnails, links, excerpts or full posts.</li>
<li>Small Footprint. Doesn’t slow down your site!</li>
<li>Automatic display of related posts after the post content.</li>
<li>Exclude or include terms and posts.</li>
<li>Search for related posts in single or multiple taxonomies and post types.</li>
<li>Limit the search for related posts by date, number or post meta.</li>
<li>Use your own HTML templates for display of the related posts.</li>
<li>Extensive <a href="http://keesiemeijer.wordpress.com/related-posts-by-taxonomy/" rel="nofollow ugc">plugin documentation</a>.</li>
<li>Follows WordPress coding standards and plugin best practices.</li>
<li>Highly Adjustable!</li>
</ul>
For the following features you need to be somewhat familiar with WordPress <a href="https://developer.wordpress.org/plugins/hooks/" rel="nofollow ugc">hooks</a>. The <a href="http://keesiemeijer.wordpress.com/related-posts-by-taxonomy/" rel="nofollow ugc">plugin documentation</a> has many examples to help you along.
Extended features:
<ul>
<li>Use a persistent cache for the related posts query. (opt-in feature)</li>
<li>Use the WordPress REST API to get related posts. (opt-in feature)</li>
<li>Load related posts after the whole page has loaded (with Ajax). (opt-in feature)</li>
<li>Use plugin functions in your theme templates to display related posts yourself.</li>
<li>Use Filters to change the default behavior of the plugin. </li>
</ul>
Follow this plugin on <a href="https://github.com/keesiemeijer/related-posts-by-taxonomy" rel="nofollow ugc">GitHub</a>. 
Search the <a href="https://keesiemeijer.github.io/related-posts-by-taxonomy" rel="nofollow ugc">code reference</a>
See the <a href="https://wordpress.org/extend/plugins/related-posts-by-taxonomy/faq/" rel="ugc">FAQ</a> to have related posts automatically display after the post content without using the shortcode or widget.
Default usage for the shortcode is:
<pre><code>[related_posts_by_tax]
</code></pre>
Attributes for the shortcode are:
<ul>
<li><code>post_id</code></li>
<li><code>taxonomies</code></li>
<li><code>post_types</code></li>
<li><code>posts_per_page</code></li>
<li><code>order</code></li>
<li><code>orderby</code></li>
<li><code>before_shortcode</code></li>
<li><code>after_shortcode</code></li>
<li><code>title</code></li>
<li><code>show_date</code></li>
<li><code>before_title</code></li>
<li><code>after_title</code></li>
<li><code>include_terms</code></li>
<li><code>include_parents</code></li>
<li><code>include_children</code></li>
<li><code>exclude_terms</code></li>
<li><code>exclude_posts</code></li>
<li><code>format</code></li>
<li><code>gallery_format</code></li>
<li><code>image_size</code></li>
<li><code>columns</code></li>
<li><code>caption</code></li>
<li><code>link_caption</code></li>
<li><code>limit_posts</code></li>
<li><code>limit_month</code></li>
<li><code>meta_key</code></li>
<li><code>meta_value</code></li>
<li><code>meta_compare</code></li>
<li><code>meta_type</code></li>
<li><code>public_only</code></li>
<li><code>include_self</code></li>
<li><code>post_class</code></li>
</ul>
Example to show 10 related posts instead of the default 5.
<pre><code>[related_posts_by_tax posts_per_page="10"]
</code></pre>
See the <a href="https://keesiemeijer.wordpress.com/related-posts-by-taxonomy/#shortcode" rel="nofollow ugc">documentation</a> for more information about these attributes.
<h4>Translations</h4>
<ul>
<li>Dutch </li>
<li>French (by <a href="http://www.artisanathai.fr" rel="nofollow ugc">Annie Stasse</a>) </li>
<li>Spanish (by <a href="http://www.ludobooks.com" rel="nofollow ugc">Ludobooks – Cuentos personalizados</a>) </li>
<li>Catalan (by <a href="http://www.ludobooks.com" rel="nofollow ugc">Ludobooks – Cuentos personalizados</a>) </li>
<li>Polish (by <a href="http://rekolekcje.net.pl" rel="nofollow ugc">koda0601</a>)</li>
</ul>

My goodness!

Display a list of related posts on your site based on the most terms in common. Supports thumbnails, shortcodes, a widget and more.

Random Related Posts Based on Category vs Related Posts by Taxonomy